Can you help interpret what this interval tells us and how I can understand it?

The 95% confidence interval for the population mean IQ is, (107.77, 116.23).

**Interpretation:**

We are 95% confident that the population mean IQ will be in between (107.77, 116.23).

**Explanation:**

The size of the sample, *n* = 33

The sample mean, $xˉ$ = 112

**The population standard deviation**, $σ$ = 12.4

Since the population standard deviation is known, use of *z* confidence interval

is appropriate in this scenario.

**The z-critical value at 95% confidence level**, $z_{∗}$ = 1.96

**The margin of error is**, $E=z_{∗}×n σ =1.96×33 12.4 =4.23$

The 95% confidence interval for the population mean IQ is,

$[xˉ−E,xˉ+E]=[112−4.23,112+4.23]=[107.77,116.23]$

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